It all comes down to a matter of prefrence. The writter of the solutions (I addition to myself) doesn't like fractions and prefers x before y.
Calculate the straight line characteristics for the following linear 1st order PDE's
I calculate and when transformed becomes
but the book its given as and when transformed becomes
I calculate when transformed becomes
but the book is when transformed becomes
The only way I can see them arriving at this is therefore
The pattern I see in these kind of questions is that when k is written in terms of x and y that the 'x' terms are always positve before transforming. Why is this?